On Random Walks with a General Moving Barrier

Zhang, Jun; Hui, Lam

doi:10.1086/499802

Cited by 63 publications

(94 citation statements)

References 28 publications

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“…It is straightforward to show that this integral equation has an analytical solution for a constant barrier [40,41], including the constant case δ Λ c ≈ 1.676 which is the ΛCDM solution. Once the first crossing distribution is found after solving this equation, the procedure would be to marginalise over the possible values of the environmental density.…”

Section: The Excursion Set Theory In F (R)mentioning

confidence: 97%

Thef(ℛ) halo mass function in the cosmic web

Braun-Bates

Winther

Alonso

et al. 2017

J. Cosmol. Astropart. Phys.

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Abstract. An important indicator of modified gravity is the effect of the local environment on halo properties. This paper examines the influence of the local tidal structure on the halo mass function, the halo orientation, spin and the concentration-mass relation. We use the excursion set formalism to produce a halo mass function conditional on large-scale structure. Our simple model agrees well with simulations on large scales at which the density field is linear or weakly non-linear. Beyond this, our principal result is that f (R) does affect halo abundances, the halo spin parameter and the concentration-mass relationship in an environment-independent way, whereas we find no appreciable deviation from ΛCDM for the mass function with fixed environment density, nor the alignment of the orientation and spin vectors of the halo to the eigenvectors of the local cosmic web. There is a general trend for greater deviation from ΛCDM in underdense environments and for high-mass haloes, as expected from chameleon screening.

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Section: The Excursion Set Theory In F (R)mentioning

confidence: 97%

Thef(ℛ) halo mass function in the cosmic web

Braun-Bates

Winther

Alonso

et al. 2017

J. Cosmol. Astropart. Phys.

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“…Our results are consistent with previous work by SvdW for sharp-k filtering and for (SX) filtering. See also Zhang & Hui (2006); for a complementary approach. Achitouv et al (2013) found that within the excursion set framework, any consistent barrier should have an intrinsic scatter due to the randomness of the position that the excursion-set theory assumes in order to compute the fraction of collapsed regions.…”

Section: Excursion Set Approachmentioning

confidence: 99%

Testing spherical evolution for modelling void abundances

Achitouv

Neyrinck

Paranjape

2015

Mon. Not. R. Astron. Soc.

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We compare analytical predictions of void volume functions to those measured from Nbody simulations, detecting voids with the zobov void finder. We push to very small, nonlinear voids, below few h −1 .Mpc radius, by considering the unsampled DM density field. We also study the case where voids are identified using halos. We develop analytical formula for the void abundance of both the excursion set approach and the peaks formalism. These formula are valid for random walks smoothed with a top-hat filter in real space, with a large class of realistic barrier models. We test the extent to which the spherical evolution approximation, which forms the basis of the analytical predictions, models the highly aspherical voids that occur in the cosmic web, and are found by a watershed-based algorithm such as zobov. We show that the volume function returned by zobov is quite sensitive to the choice of treatment of sub-voids, a fact that has not been appreciated previously. For reasonable choices of sub-void exclusion, we find that the Lagrangian density δ v of the zobov voids -which is predicted to be a constant δ v ≈ −2.7 in the spherical evolution model -is different from the predicted value, showing substantial scatter and scale dependence. This result applies to voids identified at z = 0 with effective radius between 1 and 10M pc.h −1 . Our analytical approximations are flexible enough to give a good description of the resulting volume function; however, this happens for choices of parameter values that are different from those suggested by the spherical evolution assumption. We conclude that analytical models for voids must move away from the spherical approximation in order to be applied successfully to observations, and we discuss some possible ways forward.

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“…For a more general barrier, there is no exact analytic solution, but reasonable approximations have been worked out by Sheth & Tormen, and Lam & Sheth [36,37]. In this paper, we adopt the algorithm of Zhang & Hui [38] which gives an exact, albeit numerical, solution for the unconditional f -function. It is straightforward to extend their method to the conditional case.…”

Section: F Calculating the First-crossing Distributionsmentioning

confidence: 99%

Scale-dependent halo bias from scale-dependent growth

2011

Self Cite

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We derive a general expression for the large-scale halo bias, in theories with a scale-dependent linear growth, using the excursion set formalism. Such theories include modified gravity models, and models in which the dark energy clustering is non-negligible. A scale dependence is imprinted in both the formation and evolved biases by the scale-dependent growth. Mergers are accounted for in our derivation, which thus extends earlier work which focused on passive evolution. There is a simple analytic form for the bias for those theories in which the nonlinear collapse of perturbations is approximately the same as in general relativity. As an illustration, we apply our results to a simple Yukawa modification of gravity, and use SDSS measurements of the clustering of luminous red galaxies to constrain the theory's parameters. 98.80.Es; 98.65.Dx; 95.35.+d

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On Random Walks with a General Moving Barrier

Cited by 63 publications

References 28 publications

Thef(ℛ) halo mass function in the cosmic web

Thef(ℛ) halo mass function in the cosmic web

Testing spherical evolution for modelling void abundances

Scale-dependent halo bias from scale-dependent growth

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